Bandwidth efficiency in m - ary psk

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The discussion focuses on the formulas for bandwidth efficiency in M-ary PSK, highlighting two different approaches. The first formula suggests that bandwidth efficiency is calculated as Rb/B = log2 M, where Rb is the bit rate and B is the bandwidth. However, Simon Haykin's reference indicates that the correct bandwidth efficiency is (log2 M)/2, leading to a different interpretation of the channel bandwidth required for M-ary PSK. The confusion arises from the definitions of symbol rate and channel bandwidth in relation to the bit rate. Ultimately, the thread seeks clarification on which formula accurately represents bandwidth efficiency in M-ary PSK systems.
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In M-ary psk
Rb=Rs*log M log with base 2
Rb- bit rate
Rs - symbol rate
then bandwidth required for passband signal is B=Rs
and bandwidth effeciency = Rb/B=log M log with base 2.
Is the above formula for bandwidth efficiency correct ?
But in simon haykin it is given that bandwidth efficiency is (log M )/2 log with base 2
 
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The channel bandwidth required to pass M-ary PSK is B=2/T
Now, T = Tb (log2 M) and Rb = 1/Tb
So rho = Rb/B = (log2 M) /2
 

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